Theoretical population genetics

Most of evolutionary theory considers neutral models of evolution, or selection acting on one, two, or maybe a few sites at a time. Most populations, however, are polymorphic at a large number of sites and a fraction of these sites is under selection. Furthermore, fitness might depend on particular combinations of alleles, i.e. alleles might interact and their effect is dependent on the genetic background. The large number of possible genotypes and the constant reshuffling of alleles make multi-locus evolution a challenging subject. Statistical physics, however, provides many examples how complex systems with many degrees of freedom give rise to simple macroscopic behavior. We want to explore how methods from statistical physics can help to develop a general understanding of multi-locus evolution.

Coalesce and genetic diversity in populations under selection

The genetic diversity of a species is shaped by its recent evolutionary history and can be used to infer demographic events or selective sweeps. Most inference methods are based on the null hypothesis that natural selection is a weak evolutionary force. However, many species, particularly pathogens, are under continuous pressure to adapt in response to changing environments. A statistical framework for inference from diversity data of such populations is currently lacking. Toward this goal, we explore the properties of genealogies that emerge from models of continual adaptation. We show that lineages trace back to a small pool of highly fit ancestors, in which simultaneous coalescence of more than two lineages frequently occurs. While such multiple mergers are unlikely under the neutral coalescent, thefitness_sketchy create a unique genetic footprint in adapting populations. The site frequency spectrum of derived neutral alleles, for example, is non-monotonic and has a peak at high frequencies, whereas Tajima’s D becomes more and more negative with increasing sample size. Since multiple merger coalescents emerge in various evolutionary scenarios characterized by sustained selection pressures, we argue that they should be considered as null-models for adapting populations. Remarkably rather simple scaling arguments map coalescence in sexual populations to results in asexual populations with good accuracy.

Genealogies of rapidly adapting populations
Richard Neher, Oskar Hallatschek. PNAS 110 (2), 437-442

Recombination and Epistasis

Recombination and re-assortment of chromosomes continuously reshuffle genomes in the population allowing selection to act directly on alleles and eliminate the less fit variants. Yet recombination can also be detrimental to fitness because it breaks up the combinations of alleles that interact synergistically with each other. In the presence of genetic interaction, selection and recombination therefore act as opposing forces, the former trying to enrich favorable combinations, the latter breaking them apart and producing novel variants. We study a model of natural selection in a recombining population. We find, that depending on the relative strength of epistasis and recombination, two distinct “phases” of selection appear. In one regime, recombination wins over selection and decouples the loci along the genome, such that selection operates on individual loci. In the other regime, selection is sufficiently strong to overcome recombination and amplifies fit genotypes, which then enter a competition between clonal subpopulations.

Emergence of clones in sexual populations
Richard Neher, Marjia Vucelja, Marc Mezard, Boris Shraiman. JSTAT 2013 (01), P01008

Population genetic inference

In most cases, evolution is too slow to be observed directly (HIV intra-patient evolution being a prominent exception). In such cases, parameters have to be inferred by comparing patterns of genetic diversity to expectations generated by simple models. We have developed methods to use patterns of rare variation to estimate selection coefficients of beneficial variants. We have also looked at patterns of correlated substitutions to estimate the prevalence of compensatory evolution in adaptation.
Estimating the Strength of Selective Sweeps from Deep Population Diversity Data. P.W. Messer and R.A. Neher. Genetics (2012)
Correlated Evolution of Nearby Residues in Drosophilid Proteins. B. Callahan, R.A. Neher, D. Bachtrog, P. Andolfatto, B.I. Shraiman, PLoS Genet (2011)

Deleterious Mutations and Muller’s ratchet

The majority of mutations are deleterious and the importance of deleterious mutations for the evolutionary process and their contribution to intra-species diversity have long been debated. The term “Muller’s Ratchet” has been coined to describe the phenomenon of almost irreversible (other than exact back mutation) accumulation of deleterious mutations in asexual populations. Muller’s ratchet has mostly been studiedratched in a very simple model introduced by Haigh, which despite its simplicity has resisted a satisfactory solution. We have recently made two contributions that (i) calculate the rate of Muller’s ratchet in a consistent manner, and (ii) determine how large a beneficial mutation rate is necessary to offset the ratchet.

Dynamic Mutation–Selection Balance as an Evolutionary Attractor
Sid Goyal, Dan Balick, Elisabeth Jerison, Richard Neher, Boris Shraiman, Michael Desai. Genetics 191 (4), 1309-1319
Fluctuations of Fitness Distributions and the Rate of Muller’s Ratchet
Richard Neher, Boris Shraiman. Genetics. 191 (4), 1283-1293